What is the Greatest Common Factor of 52309 and 52320?

Greatest common factor (GCF) of 52309 and 52320 is 1.

GCF(52309,52320) = 1

We will now calculate the prime factors of 52309 and 52320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52309 and 52320.

How to find the GCF of 52309 and 52320?

We will first find the prime factorization of 52309 and 52320. After we will calculate the factors of 52309 and 52320 and find the biggest common factor number .

Step-1: Prime Factorization of 52309

Prime factors of 52309 are 17, 181. Prime factorization of 52309 in exponential form is:

52309 = 17² × 181¹

Step-2: Prime Factorization of 52320

Prime factors of 52320 are 2, 3, 5, 109. Prime factorization of 52320 in exponential form is:

52320 = 2⁵ × 3¹ × 5¹ × 109¹

Step-3: Factors of 52309

List of positive integer factors of 52309 that divides 52309 without a remainder.

1, 17, 181, 289, 3077

Step-4: Factors of 52320

List of positive integer factors of 52320 that divides 52309 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 109, 120, 160, 218, 240, 327, 436, 480, 545, 654, 872, 1090, 1308, 1635, 1744, 2180, 2616, 3270, 3488, 4360, 5232, 6540, 8720, 10464, 13080, 17440, 26160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52309 and 52320. The biggest common factor number is the GCF number.
So the greatest common factor 52309 and 52320 is 1.

Also check out the Least Common Multiple of 52309 and 52320